Question

What is the answer and how do i solve it?

Answer 1

Step-by-step explanation

Since we have the expression:

`(x)/(x^2+x-6)-(2)/(x+3)`

First, we need to find the least common multiplier as follows:

Least common multiplier of x^2 + x - 6, x+3: (x-2)(x+3)

Ajust fractions based on the LCM:

`=(x)/(\left(x-2\right)\left(x+3\right))-(2\left(x-2\right))/(\left(x-2\right)\left(x+3\right))`
`\mathrm{Apply\: the\: fraction\: rule}\colon\quad (a)/(c)-(b)/(c)=(a-b)/(c)`
`=(x-2\left(x-2\right))/(\left(x-2\right)\left(x+3\right))`
`Expand\text{ x-2(x-2)}`
`=(-x+4)/(\left(x-2\right)\left(x+3\right))`

The final expression is as follows:

`=(-x+4)/((x-2)(x+3))`